Jon Heyman of the MLB Network reported Tuesday the Rockies don't currently have the budget flexibility to make an offer to Story, who can become a free agent after the 2021 season.
The 28-year-old Texas native burst on to the scene with 27 home runs in just 97 appearances during his 2016 rookie season, and he really hasn't stopped slugging ever since.
Story has posted a .277/.343/.535 triple-slash line with 134 homers and 80 stolen bases in 603 regular-season games over the past five years. His 17.9 WAR over that time span ranks fifth among MLB shortstops, per FanGraphs.
He explained when spring training got underway last week that he's focused on the upcoming season, not his contract situation.
"I'm focused on personally being the best teammate I can be," Story told reporters. "I try not to look too far ahead. I'm trying to be where my feet are, which is right here in spring training with the Rockies."
He'll carry an even larger offensive burden for Colorado in 2021 after standout third baseman Nolan Arenado was traded to the St. Louis Cardinals during the offseason.
If the Rockies' financial outlook in wake of the COVID-19 pandemic doesn't improve by July and a lucrative, long-term extension isn't feasible, the question becomes whether the front office becomes aggressive in trying to trade Story to a contender before he can hit the free-agent market.
Colorado was able to obtain four prospects and 27-year-old left-hander Austin Gomber, who posted a 1.86 ERA in 14 appearances (four starts) last season, for Arenado and could further bolster the depth in its system with a Story blockbuster before the July 31 deadline.
Whether the Rockies are still in playoff contention as that date moves closer will also be a factor. The team was 26-34 last year, finishing fourth in the NL West.
Story and Co. open the 2021 campaign April 1 against the reigning World Series champion Los Angeles Dodgers.